This invention relates to a high damping alloy which is capable of, when used as parts for a compression and the other devices, absorbing vibrations and noises generated from these devices. Noises have recently been regarded as one of major public nuisances. Therefore, attempt has been made to reduce noises as generated from a variety of devices. As one method for absorbing vibrations and noises, a high damping material is employed for such a purpose. As such a high damping material, plastics has been used. Since, however, plastics is lower in its mechanical strength and heat resistance, the range of application is restricted with the resultant disadvantage. To avoid this drawback, a metal material having a high damping capability has been desired. Recently, a copper alloy including 40-60% of Mn has been developed. With such an Mn-Cu alloy, however, a high damping capability is exhibited at a temperature close to room temperature, but the transitiin temperature of the damping capability is low i.e. 50.degree. to 80.degree. C. and the damping capability is suddenly lowered at a temperature higher than this transition temperature. For this reason, the alloy is not suitable as a damping member, such as a valve seat for a compressor, which is subjected to a heat of about 100.degree. C.